Stability of high-speed compressible rotating Couette flow

Abstract

In this study, the linear stability of high-speed, rotating Couette flow to two- and three-dimensional disturbances in unite-gap spacings, including the full effects of compressibility and viscosity, is considered. Particularly, the combined effects of Mach number, Reynolds number, radial heating, and gap spacing are investigated. For a stationary outer cylinder, the primary instability is an axisymmetric mode independent of the Mach number. Increasing Mach numbers have a destabilizing effect for wide gaps, and a stabilizing effect for narrow gaps. For a sufficiently fast, counter-rotating outer cylinder, the primary instability becomes a three-dimensional traveling wave. Compressibility has a stabilizing effect on these modes regardless of the gap width; also, heating at the outer cylinder stabilizes the flow. Bicritical points for the primary instability corresponding to the crossover of the azimuthal wave numbers are determined for cylinders counter-rotating with equal angular speed. © 1993 American Institute of Physics.